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Lecture16– DynamicProgrammingReading:KTSections6.1and6.2

Partialcontentoftheseslideshavebeenobtainedfromtheofficiallectureslidesthataccompanythetextbook.Acompletesetofslidescanbefoundat:http://www.cs.princeton.edu/~wayne/kleinberg-tardos/

Algorithmtechniques

Datastructures•Useextradatastructures• Exploitthestructuretoimprovecomplexity

Greedyalgorithms•Buildupasolutionincrementally•Myopicallyoptimizingsomelocalcriterion

Divideandconquer•Breakupaproblemintoindependentsubproblems• Solveeachsubproblem•Combinesolutionstosubproblemstoformsolutiontooriginalproblem

DynamicProgramming•Breakupaproblemintoaseriesofoverlappingsubproblems

•Buildupsolutionstolargerandlargersubproblems

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Abitofhistory

WeightedIntervalSchedulingproblem

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WeightedIntervalSchedulingproblem

Let’strysolvingit

• Willgreedywork?

• Howaboutdivideandconquer?

• Istheresomestructureintheproblemthatwecanexploit?

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Let’sdefineafewnotions

Morenotations

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Abruteforcesolution

What’sthecomplexityofthisalgorithm?

Memoization

What’sthecomplexityofthisalgorithm?

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Bottom-updynamicprogramming